Renaissance(1300-1700)

1. Leonardo Da Vinci (1452 - 1519)

The legendary artist and master of anatomy (painter of the Mona Lisa and Last Supper), De Vinci also invented the first hydraulic machine, boat, design of a flying machine, crane clocks, autonomous humanoid robot, and countless war machines. The father of modern science made large leaps ahead of his time in physics, engineering, aeronautics, and astronomy. He was famous for his mirror-writing (probably because he was left- handed) and his exquisitely detailed drawings and notebooks.

Leonardo da Vinci undertook one of the greatest study of light and dark. In countless notes and drawings, he analyzed the effects of light and shade in nature and in art. Leonardo's drawings of shadow projections largely employ a format from using just a single light source. He studied the problems of shadows cast by both simple and non-spherical obstacles.

Leonardo's experimentation followed clear scientific method approaches, and his theorizing and hypothesizing integrated the arts and particularly painting; these, and Leonardo's unique integrated, holistic views of science make him a forerunner of modern systems theory and complexity schools of thought.

2. Nicolaus Copernicus (1473 – 1543)

Nicolaus Copernicus, was the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe. His book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) – released on the day of his death - is regarded by many to be the starting point of modern astronomy. By postulating only the rotation of the Earth, revolution about the sun, and tilt of Earth's rotational axis, Copernicus could explain the observed motion of the heavens. Since Copernicus worked out his system in full mathematical detail, his most significant achievement was his combination of mathematics and physics unlike Ptolemy who regarded his model as a mathematical tool with no physical reality; or Aristarchus who proposed a physical system with no mathematical support.

The results of his observations of Mars and Saturn in this period, and especially a series of four observations of the Sun made in 1515, led to discovery of the variability of Earth's eccentricity and of the movement of the solar apogee in relation to the fixed stars.

3. Tycho Brahe (1546–1601), born Tyge Ottesen Brahe

Known today for his unprecedented dedication to accurate astronomical observation, Tycho Brahe was a Danish nobleman who brought many commendable contributions to the development of modern astronomy. He built his observatory, Uraniborg, on an island off the Swedish coast. Tycho lost part of his nose in a drunken duel in 1566 and constructed his own prosthetic nose of copper. Tycho served as the imperial mathematician to Rudolph II.

Among the first to make nightly observations from the same place, at the same time every night, Brahe is regarded by many as one of the best astronomical observers in all recorded history. Furthermore, he was the last of the major naked eye astronomers, working without telescopes for his observations. With his meticulous methodology, advanced astronomical tools and constant calibrations of the stars and planets, he brought a new attention to the accuracy of astronomical readings. His data was used by his assistant Kepler to derive the laws of planetary motion.

4. Johannes Kepler ( 1571–1630)

Initially in his defense of the Copernican system, Kepler studied the five Platonic solids as a method of achieving the orbitals paths of Mercury, Venus, Earth, Mars, Jupiter, and Saturn. He discovered that they could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets. By ordering the solids correctly— octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, because it was not precise enough. His work was published as The Sacred Mystery of the Cosmos in 1596.

Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Verifying this relationship throughout the orbital cycle required extensive calculations; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times—Kepler's second law of planetary motion. Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler was armed with Tycho's irrefutable data — Kepler had served as Tycho’s assistant from 1600 until Brahe’s death in 1601 and was subsequently named as Brahe’s successor as imperial mathematician in the court of Emperor Rudolph II.

In early 1605 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Based on Brahe's data and Kepler's dogged determination to get it right he discovered that an elliptical orbit fit the Mars data. He immediately concluded that all planets move in ellipses, with the sun at one focus—Kepler's first law of planetary motion. For his third law of planetary motion, he tried many combinations until he discovered that "The square of the periodic times are to each other as the cubes of the mean distances."

Between 1615 and 1620 Kepler wrote the three volumes of The Epitome of Copernican Astronomy. Despite the title, Kepler's textbook culminated in his own ellipse-based system. In 1827, he published the Rudolphine Tables which consisted of a star catalogue and planetary tables using some observation data collected by Tycho Brahe

In addition, Kepler studied optics and developed the concept of rays. He improved the early telescopes, invented a convex eyepiece and discovered a means of determining the magnifying power of lenses. He wrote Conversation with the Starry Messenger in support of Galileo’s discovery of the moons of Jupiter.

5. Galileo Galilei (1564– 1642)

Galileo described dynamics and statics and emphasized the use of mathematics. Galileo showed that all bodies fall at the same rate regardless of mass which directly refuted. Aristotelian physics which assumed that speed of fall is proportional to weight. Galileo also determined a formula for calculating the period of a pendulum. He said that motion is continuous and can only be altered by the application of a force. He understood the parabola, both in terms of conic sections and in terms of the y varies with x². Galileo further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of friction and other disturbances. He maintained that for distances up to the range of the artillery of his day, the deviation of a projectile's trajectory from a parabola would only be very slight. Galileo perfected the astronomical telescope – producing images that were upright instead of being inverted.

He promoted the Copernican, heliocentric theory of the solar system which was supported by his telescopic observations of three of the four largest satellites of Jupiter. This fact totally upended Aristotelian cosmology – which stated that all planets orbited the Earth. A year and a half later, he had compiled enough data to determine each moon’s orbital period. He also observed the phases of Venus, a fact predicted by Copernican theory but impossible to explain with Ptolemy’s model.

He also used his telescope to see sunspots and craters on the moon which revealed yet another flaw of Aristotelian cosmology. All astronomical bodies were supposed to be composed of materials altogether different from those found on the earth (quintessence); a fact that was evidently no longer accurate. He also used his telescope to determine that the Milky Way was a collection of unique stars, invisible to the naked eye.

In 1632, Galileo pushed his book, Dialogue Concerning the Two Chief World Systems, in which Simplicio, the defender of the Aristotelian Geocentric view, was often caught in his own errors and sometimes came across as a fool. This portrayal of Simplicio made A Dialogue appear as an advocacy book: an attack on Aristotelian geocentrism and defense of the Copernican theory. Unfortunately for his relationship with the Pope, Galileo put the words of Urban VIII into the mouth of Simplicio. As expected the Pope did not take the suspected public ridicule lightly, nor the Copernican advocacy. In 1633, he was tried by the Inquisition, found "vehemently suspect of heresy" and forced to recant that the earth moved around the sun. Although sentenced to formal imprisonment, Galileo was allowed to spend the rest of his life under house arrest under his daughter’s care until his death in 1642.

6. René Descartes (1596 – 1650)

Descartes suggested the idea of algebraically representing geometry in terms of coordinates; today his axis system is used by mathematicians interested in the Cartesian plane, or “xy-plane.”

Descartes saw that a point in a plane could be completely determined if its distances (conventionally 'x' and 'y') were given from two fixed lines drawn at right angles in the plane, with the now-familiar convention of interpreting positive and negative values. Conventionally, such co-ordinates are referred to as "Cartesian co-ordinates". Descartes also asserted that a point in 3-dimensional space could be determined by three co-ordinates.

He also "pioneered the standard notation" that uses superscripts to show the powers or exponents, for example the 4 used in x4 to indicate squaring of squaring

He is remembered for the philosophical phrase: "cogito ergo sum" -- I think therefore I am.

7. Blaise Pascal (1623 –1662)

Pascal invented a simple method now known as Pascal’s Triangle to determine the probability of certain outcomes. In 1642, while still a teenager, he started work on developing a calculating machine, and after three years of effort and 50 prototypes he invented the mechanical calculator (called the Pascaline), taking a large step towards complex, large scale computations.

Pascal was an important mathematician, helping to create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. .Pascal's development of probability theory was his most influential contribution to mathematics. Originally applied to gambling, today it is extremely important in economics, especially in actuarial science

His inventions include the hydraulic press (using hydraulic pressure to multiply force) and the syringe. His name has been immortalized as the metric unit of pressure, a programming language, and Pascal's Law of Hydrostatics.

8. Christiaan Huygens (1629 – 1695)

Huygens was a Dutch astronomer, mathematician and physicist who proposed a wave theory of light. In 1656 he invented a pendulum clock which became the first mechanical clock to greatly increase time measurements. In the early 1650s he and his elder brother discovered a new method of grinding and polishing lenses, and in 1655, with one of his lenses, he discovered Titan, a moon orbiting Saturn, along with the rings of Saturn. He also observed the surface of Mars and the nebula in the constellation of Orion.

At the urging of Pascal, Huygens published his work on probability theory. He derived the formula for a simple pendulum, stated that the center of gravity moves uniformly in a straight line, and found the mathematical expression for centrifugal force. But he disagreed with Newton's theory of gravity.

Huygens worked out an alternative theory that showed how light could be thought of as a wave which pulsated longitudinally in the overall direction of its motion. Thomas Young’s double slit interference experiment vindicated Huygens’ wave theory. Huygens also investigated birefringence (double refraction) in calcite crystals and correctly explained the phenomena as the polarization of light.

9. Robert Hooke (1635– 1703)

As an assistant to Robert Boyle from 1655 to 1662, Hooke's particularly keen eye, adept mathematics most likely resulted in his making the observations and developing the mathematics of Boyle's Law. Hooke became Curator of Experiments in 1662 to the Royal Society, and took responsibility for all experiments performed at its weekly meetings. This was a position he held for over 40 years and which kept him in the thick of science throughout Britain and beyond. There are no known authenticated portraits of Hooke.

Hooke developed the balance spring independently discovered the law of elasticity which bears his name and which describes the linear variation of tension with extension in an elastic spring. He used his knowledge to develop a pocket watch that used a balance-spring instead of a pendulum.

He also invented the universal joint, which is a key component of the modern car and the air-pump which was the ancestor of the steam engine and internal combustion engine.

Hooke wrote the first book describing observations made with a microscope and was also the first person to use the term “cell” to identify microscopic structures.

10. Gottfried Wilhelm Leibniz ( 1646 – 1716)

Gottfried Wilhelm Leibniz was a philosopher, mathematician, physicist, jurist, and contemporary of Newton. The 20th century philosopher and mathematician Bertrand Russell considered Leibniz's greatest claim to fame to be his invention of the infinitesimal calculus -- a remarkable achievement considering that Leibniz was self-taught in mathematics.

Although the historical records suggest that Newton developed his version of calculus first, Leibniz was the first to publish. Unfortunately this resulted in a rancorous dispute that raged for decades, pitting English continental mathematicians supporting Newton against continental mathematicians supporting Leibniz. Today, they are generally recognized as co-inventors but Leibniz' notation for calculus, including the integral sign and derivative notation, was far superior to that of Newton and is still in use today.

In 1673, Leibniz described an arithmetic machine, called the Stepped Reckoner that would make calculations easy, fast, and reliable. He hired a clockmaker to make the first brass prototype. He presented the machine to the French Academy of Sciences in 1675, after which he wrote:

I managed to build such arithmetic machine, which is completely different of the machine of Pascal, as it allows multiplication and division of huge numbers to be done momentarily, without using of consecutive adding or subtraction, and to other correspondent, the philosopher Gabriel Wagner—I managed to finish my arithmetical device. Nobody had seen such a device, because it is extremely original.

Leibniz died embittered, in ill health, and without achieving the considerable wealth, fame, and honor accorded to Newton. Although Much of his' work went unpublished during his lifetime. his diverse writings were resurrected and published in the late 19th and 20th centuries. But calculus -- with Leibniz notation still in use today -- remains his towering legacy.

11. Sir Isaac Newton (1642 – 1727)

Edmond Halley encouraged Newton to publish his calculations, and in 1687 Philosophiae Naturalis Principia Mathematica, was published. This is probably the most important and influential work on physics of all times.

 The first book of Principia explained Newton's three laws of motion (inertia, acceleration, and action/reaction).  In the second book he stated explicit principles of scientific methods which applied universally to all branches of science, and  In book three he proposed a universal gravitational force with which he could explain the causes of the tides and their major variations, the precession of the Earth's axis, and the motion of the moon and the planets.

Newton is considered to be the co-inventor of differential and integral calculus with Leibniz. He invented the first reflecting telescope. He also observed that white light from the sun changed into a spectrum of colors when the beam passed a glass prism. He believed that light consisted of small particles, or corpuscles, and that white light really was a mixture of different types of corpuscles. Newton retired in 1693 after suffering a nervous breakdown, Opticks was not published until 1704.